Systems and Methods for Generating and Steering Orbital Angular Momentum Electromagnetic Beams

This application is a continuation of International Application No. PCT/CN2023/136126, entitled “SYSTEMS AND METHODS FOR GENERATING AND STEERING ORBITAL ANGULAR MOMENTUM ELECTROMAGNETIC BEAMS,” filed on Dec. 4, 2023, which application is hereby incorporated herein by reference in its entirety.

The technical field generally relates to wireless communications, and more particularly to systems and methods for generating and steering orbital angular momentum (OAM) electromagnetic beams.

Continued growth in the number of mobile device users and the demand for higher data transfer rates and adequate bandwidth capacities in free-space line-of-sight communication links have increased the importance of multimedia services and mobile Internet in wireless communication systems. One method that attempts to address these needs is through space-division multiplexing (SDM), which allows multiple, orthogonal, data-carrying beams to be transmitted at the same time and over the same frequency between a single transceiver pair. According to this method, each beam occupies an individual spatial mode in an orthogonal basis set. SDM can be achieved using mode-division-multiplexing (MDM). One spatial mode basis that has been demonstrated for use of MDM in free-space line-of-sight communication links is that of orbital angular momentum (OAM) modes. An OAM electromagnetic beam includes a phase front with an azimuthally varying phase given by exp(ikφ), where k is the OAM order (k=0, ±1, ±2, . . . ) and φ is the azimuthal angle. For |k|≥1, the phase front according to a helical phase structure as the OAM electromagnetic beam propagates.

Precise alignment between transmitters and receivers in communication systems plays an important role to ensure that adequate signal power is received at the receiver. For OAM multiplexing systems, precise alignment is often of even greater importance since misalignment may lead to crosstalk among channels. Accordingly, a transmitter should be able to both generate and steer OAM electromagnetic beams for active pointing. The few OAM-based beam-scanning systems that have been reported in the literature tend to be complex, costly, manual (non-electronic), and suffer from limited scan range and/or poor radiation performance (e.g. deteriorated side lobe level, insufficient directivity, high loss, low efficiency, and/or poor phase calibration quality). Despite advances in the field, challenges remain in the development of beam generation and steering techniques for OAM electromagnetic beams.

The present disclosure generally relates to techniques, including systems and methods, for generating and steering orbital angular momentum (OAM) electromagnetic beams.

The disclosed embodiments generally use a beamforming device, a beamsteering device, a slotted antenna structure. The beamforming device generates beamforming signals modulated in accordance with beamforming phase shifts related to a mode content of the OAM beam. The beamsteering device generates beamsteering signals by modulating beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM beam. The slotted antenna structure is fed with the beamsteering signals to emit the OAM beam. The slotted antenna structure includes at least one slotted radial waveguide azimuthally partitioned into waveguide sectors by partition walls. Waveguide sectorization allows for the OAM beam to be steered by providing the different waveguide sectors with different beamsteering signals associated with different beamsteering phase shifts. Advantageously, the OAM beam may carry a relatively large number of OAM modes and may be steerable through 360° in azimuth and up to 10° in elevation. The disclosed embodiments may be used in both in a transmit mode and a receive mode.

In some embodiments, the radial extent of the partition walls is less than that of the cavity, corresponding to a partial waveguide sectorization. Partial waveguide sectorization can improve the radiation performances of the antenna structure compared to a full waveguide sectorization, for example, in terms of suppressing or at least reducing grating lobes and/or side lobes.

In some embodiments, the antenna structure is provided with multiple sectorized waveguides, whether with partial or full sectorization. In such embodiments, multiple sectorized waveguides may be stacked concentrically in a nested arrangement in order for the radiating surfaces of the multiple sectorized waveguides to be coplanar with each other in order to provide the antenna with a flat radiating surface. Such an arrangement can achieve several advantages compared to a multilevel arrangement of the waveguide's radiating surfaces. Examples of such advantages can include (i) a reduction in unwanted reflections and other radiation performance deterioration caused by near-field interference effects between OAM modes emitted by different waveguides, (ii) an improvement in load impedance uniformity and impedance matching, and (iii) a more compact packaging arrangement

In accordance with an aspect, there is provided a system for generating and steering an OAM electromagnetic beam. The system includes a beamforming device configured to receive a plurality of input signals and output a plurality of beamforming signals by modulating the plurality of input signals in accordance with beamforming phase shifts related to a mode content of the OAM electromagnetic beam. The system also includes a beamsteering device configured to receive the plurality of beamforming signals and output a plurality of beamsteering signals by modulating the plurality of beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM electromagnetic beam. The system further includes an antenna structure having a radial waveguide. The radial waveguide includes a base plate and a slot plate defining a waveguide cavity therebetween. The slot plate has a plurality of radiating slots formed therethrough. The radial waveguide is also partitioned into a plurality of waveguide sectors by a plurality of azimuthally spaced partition walls. Each partition wall extends radially over less than a radial extent of the waveguide cavity, which provides partial waveguide sectorization. Each waveguide sector includes a feed probe connected to the beamsteering device. Each feed probe is configured to introduce a corresponding one of the plurality of beamsteering signals into the waveguide sector and cause the corresponding beamsteering signal to radiate through a number of the radiating slots corresponding to the waveguide sector. The output from all the waveguide sectors generates the OAM electromagnetic beam.

In accordance with another aspect, there is provided a method of generating and steering an OAM electromagnetic beam. The method includes a step of generating a plurality of beamforming signals by modulating a plurality of input signals in accordance with beamforming phase shifts related to a mode content of the OAM electromagnetic beam. The method also includes a step of generating a plurality of beamsteering signals by modulating the plurality of beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM electromagnetic beam. The method further includes a step of emitting the OAM electromagnetic beam according to the steering conditions by feeding the plurality of beamsteering signals to an antenna structure including a radial waveguide. The radial waveguide includes a base plate and a slot plate defining a waveguide cavity therebetween. The slot plate has a plurality of radiating slots formed therethrough. The radial waveguide is partitioned into a plurality of waveguide sectors by a plurality of azimuthally spaced partition walls. Each partition wall extends radially over less than a radial extent of the waveguide cavity, which provides partial waveguide sectorization. The step of emitting the OAM electromagnetic beam includes introducing a corresponding one of the plurality of beamsteering signals into each waveguide sector to cause the corresponding beamsteering signal to radiate through a number of the radiating slots corresponding to the waveguide sector. The output from all the waveguide sectors generates the OAM electromagnetic beam.

In accordance with another aspect, there is provided a system for generating and steering an OAM electromagnetic beam. The system includes a beamforming device configured to receive a plurality of input signals and output a plurality of beamforming signals by modulating the plurality of input signals in accordance with beamforming phase shifts related to a mode content of the OAM electromagnetic beam. The system also includes a beamsteering device configured to receive the plurality of beamforming signals and output a plurality of beamsteering signals by modulating the plurality of beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM electromagnetic beam.

The system further includes an antenna structure that includes a first radial waveguide and a second radial waveguide. The second radial waveguide azimuthally encloses the first radial waveguide. The first radial waveguide includes a first base plate and a first slot plate defining a first waveguide cavity therebetween. The first slot plate has a plurality of first radiating slots formed therethrough. The first radial waveguide is partitioned into a plurality of first waveguide sectors by a plurality of azimuthally spaced, radially extending first partition walls. Each first waveguide sector includes a first feed probe connected to the beamsteering device and configured to introduce a corresponding one of a first subset of the plurality of beamsteering signals into the first waveguide sector and cause the corresponding beamsteering signal to radiate through a number of the first radiating slots corresponding to the first waveguide sector. The output from all the first waveguide sectors generates a first beam component of the OAM electromagnetic beam.

The second radial waveguide includes a second base plate and a second slot plate defining a second waveguide cavity therebetween. The second slot plate has a plurality of second radiating slots formed therethrough. The second radial waveguide is partitioned into a plurality of second waveguide sectors by a plurality of azimuthally spaced, radially extending second partition walls. Each second waveguide sector includes a second feed probe connected to the beamsteering device and configured to introduce a corresponding one of a second subset of the plurality of beamsteering signals into the second waveguide sector and cause the corresponding beamsteering signal to radiate through a number of the second radiating slots corresponding to the second waveguide sector. The output from all the second waveguide sectors generates a second beam component of the OAM electromagnetic beam. The first slot plate defines a first radiating surface, the second slot plate defines a second radiating surface, and the first radiating surface and the second radiating surface are substantially coplanar with each other. This provides the antenna structure with a substantially flat radiating surface.

In accordance with another aspect, there is provided a method of generating and steering an OAM electromagnetic beam. The method includes a step of generating a plurality of beamforming signals by modulating a plurality of input signals in accordance with beamforming phase shifts related to a mode content of the OAM electromagnetic beam. The method also includes a step of generating a plurality of beamsteering signals by modulating the plurality of beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM electromagnetic beam. The method further includes a step of emitting the OAM electromagnetic beam according to the steering conditions by feeding the plurality of beamsteering signals to an antenna structure that includes a first radial waveguide and a second radial waveguide. The second radial waveguide azimuthally encloses the first radial waveguide.

The first radial waveguide includes a first base plate and a first slot plate defining a first waveguide cavity therebetween. The first slot plate has a plurality of first radiating slots formed therethrough. The first radial waveguide is partitioned into a plurality of first waveguide sectors by a plurality of azimuthally spaced, radially extending first partition walls. The second radial waveguide includes a second base plate and a second slot plate defining a second waveguide cavity therebetween. The second slot plate has a plurality of second radiating slots formed therethrough. The second radial waveguide is partitioned into a plurality of second waveguide sectors by a plurality of azimuthally spaced, radially extending second partition walls. The first slot plate defines a first radiating surface, the second slot plate defines a second radiating surface, and the first radiating surface and the second radiating surface are substantially coplanar with each other. This provides the antenna structure with a substantially flat radiating surface.

The step of emitting the OAM electromagnetic beam includes an operation of introducing a corresponding one of a first subset of the plurality of beamsteering signals into each first waveguide sector to cause the corresponding beamsteering signal to radiate through a number of the first radiating slots corresponding to the first waveguide sector. This generates a first beam component of the OAM electromagnetic beam. The step of emitting the OAM electromagnetic beam also includes an operation of introducing a corresponding one of a second subset of the plurality of beamsteering signals into each second waveguide sector to cause the corresponding beamsteering signal to radiate through a number of the second radiating slots corresponding to the second waveguide sector. This generates a second beam component of the OAM electromagnetic beam.

Other features, aspects, and advantages of the present disclosure will become more apparent upon reading of the following non-restrictive description of specific embodiments thereof, given by way of example only with reference to the appended drawings. Although specific features described in the foregoing summary and in the following detailed description may be described with respect to specific embodiments or aspects, it should be noted that these specific features may be combined with one another unless explicitly stated otherwise herein.

The present disclosure generally relates to techniques, which include systems and methods, for generating and steering multimode orbital angular momentum (OAM) electromagnetic beams in wireless communications applications.

The disclosed techniques may find use in various applications, industries, and wireless technologies that may need or benefit from steerable OAM electromagnetic beams for point-to-point wireless communications in either fixed or mobile applications.

1 FIG. 1 FIG. 100 102 100 104 106 108 110 100 100 Referring to, there is shown a schematic block diagram of a systemfor generating and steering an electromagnetic beamcarrying one or more OAM modes (an “OAM beam”), in accordance with an embodiment. The systemgenerally includes a beamforming device, a beamsteering device, an antenna structure, and a controller. The structure, configuration, and operation of these components and other possible components of, or coupled to, the systemare described in greater detail below. It is appreciated that, and likewise for other figures described below, are meant to provide schematic representations that aim to illustrate a number of components and features of the system, such that additional components and features that may be useful or necessary for practical operation may not be specifically depicted.

102 102 The term “electromagnetic” is intended to refer herein to radiation in any appropriate region of the electromagnetic spectrum. In some embodiments, the OAM beammay have a wavelength ranging from about 0.3 mm to about 300 mm (corresponding to a frequency ranging from about 1 GHz to 1 THz), although other embodiments may operate within other wavelength ranges. In some embodiments, the number of OAM modes carried by the OAM beammay range from one to about twenty, although a greater number of OAM modes is contemplated in other embodiments.

104 102 104 104 112 114 104 116 112 102 The beamforming deviceis configured to set the one or more OAM to be carried by the OAM beam. The beamforming deviceincludes a number of input ports and a number of output ports. The beamforming deviceis configured to receive, at its input ports, a plurality of input signals. The input signals may be generated by, and received from, an external source, such as an electromagnetic wave generator or another suitable device. In some embodiments, the input signals may have the same frequencies but different phases and/amplitudes. The beamforming deviceis also configured to output, at its output ports, a plurality of beamforming signalsby modulating the plurality of input signalsin accordance with beamforming phase shifts related to a mode content of the OAM beam.

104 104 112 116 102 100 The beamforming devicemay include one or more Butler matrices. A Butler matrix is a type of beamforming network made of passive devices such as directional couplers and phase shifters. A Butler matrix generally includes M input ports and M output ports, where M is a power of two (e.g., 2, 4, 8, 16, 32, . . . ). For each input signal, the Butler matrix is configured to output M output signals with relative phase shifts between. In the case of simultaneous excitation of m input ports (1<m≤M), the Butler matrix is configured to output a multiplexed compound signal composed of m groups of M output signals. In other embodiments, the beamforming devicemay be based on other suitable types of beamforming network architectures (e.g. Rotman lenses, Blass matrices, Nolen matrices) operable to modulate the plurality of input signalsin order to output the plurality of beamforming signalsin accordance with phase-shift schemes related to the OAM modes to be carried by the OAM beamgenerated by the system. It is appreciated that the theory, design, instrumentation, and operation of beamforming networks—including those based on Butler matrices, Rotman lenses, Blass matrices, and Nolen matrices—are generally known in the art and need not be described in detail herein other than to facilitate an understanding of the disclosed techniques.

106 102 106 106 104 106 116 104 106 118 118 118 118 102 The beamsteering deviceis configured to electronically steer (as opposed to mechanically steer) the beam direction of the OAM beamin accordance with beamsteering conditions. The beamsteering deviceincludes a number of input ports and a number of output ports. The input ports of the beamsteering deviceare coupled with the output ports of the beamforming device. The beamsteering deviceis configured to receive, at its input ports, the plurality of beamforming signalsfrom the beamforming device. The beamsteering deviceis also configured to output, at its output ports, a plurality of beamsteering signals. The plurality of beamsteering signalsis obtained by modulating the plurality of beamforming signalsin accordance with beamsteering phase shifts. The beamsteering phase shifts imposed to the beamsteering signalsare related to the steering conditions to be imparted to the OAM beam. In some embodiments, setting or adjusting the steering conditions can include setting or adjusting the beam direction within an azimuth angle steering range ranging from about 0° to about 360° and/or setting or adjusting the beam direction within an elevation angle steering range ranging from about 0° to about 10°.

118 106 104 102 106 102 118 118 It is appreciated that each beamsteering signaloutputted by the beamsteering devicehas two respective phase shifts associated with it, namely, a first phase shift imparted by the beamforming deviceand related to the mode content of the OAM beam, and a second phase shift imparted by the beamsteering deviceand related to the steering direction of the OAM beam. The plurality of beamsteering signalsmay, but need not, all have the same amplitude, and likewise for any subset of the beamsteering signals.

106 116 104 118 102 100 The beamsteering devicemay be implemented as a network or array of active or passive, analog or digital, variable phase shifters, or any other suitable type of beamsteering architecture operable to modulate the plurality of beamforming signalsreceived from the beamforming devicein order to output the plurality beamsteering signalswith relative phase shifts related to the beamsteering conditions to be imparted to the OAM beamgenerated by the system. It is appreciated that the theory, design, instrumentation, and operation of beamsteering devices, including those based on phase-shifter arrays, are generally known in the art and need not be described in detail herein other than to facilitate an understanding of the disclosed techniques.

108 118 106 102 108 120 120 102 The antenna structureis configured to receive the plurality of beamsteering signalsfrom the beamsteering deviceand generate therefrom the OAM beam. The antenna structurecan include one or more radial waveguides. In the case of multiple radial waveguides, each radial waveguide is configured to generate a corresponding beam component of the OAM beam. Each beam component can carry one or more OAM modes, including zeroth order and non-zeroth order OAM modes.

120 120 120 108 118 102 102 118 The or at least one radial waveguideis sectorized into a plurality of waveguide sectors. The number of waveguide sectors for each radial waveguidemay range between 4 and 1028. In some embodiments, the number of waveguide sectors may be a power of two (e.g., 2, 4, 8, 16, 32, . . . ), but this is not a requirement. Each waveguide sector of the or each sectorized radial waveguideof the antenna structureis configured to receive a corresponding one of the plurality of beamsteering signalsfor propagating therein and radiating therefrom, thereby generating a corresponding portion of the OAM beam. Waveguide sectorization allows for the OAM beamto be steered. This is because different waveguide sectors having different angular orientations are fed with different beamsteering signalshaving different beamsteering phase shifts imparted thereto.

110 100 4 106 110 104 112 102 110 106 116 102 The controlleris configured to control, monitor, and/or coordinate the operation of various components of, or coupled to the system, such as the beamforming deviceand the beamsteering device. The controllermay be configured to set or adjust the beamforming phase shifts imparted by the beamforming deviceon the plurality of input signalsto define or change the mode content of the OAM beam. The controllermay also be configured to set or adjust the beamsteering phase shifts imparted by the beamsteering deviceon the plurality of beamforming signalsto define or change the steering conditions for the OAM beam.

110 110 110 100 110 100 100 100 100 110 122 124 110 The controllermay be provided within one or more general-purpose computers or within any other suitable computing devices. The controllermay be implemented in hardware, software, firmware, or any combination thereof. The controllermay be connected to various components of the systemvia wired and/or wireless communication links to send and/or receive various types of signals. Non-limiting examples of signals include control signals, timing signals, and data signals. The controllermay be controlled by direct user input and/or by programmed instructions. The controllermay include an operating system for controlling and managing various functions of the system. The controllermay be fully or partly integrated with, or physically separate from, the other hardware components system. The controllermay include a processorand a memory. In some embodiments, the controllermay be implemented as a field programmable gate arrays (FPGA), an application-specific integrated circuit (ASIC), or a microcontroller.

2 2 FIGS.A-G 1 FIG. 2 2 FIGS.A-G 108 108 100 108 120 120 120 120 120 126 108 120 120 120 120 120 1-3 1 2 3 1-3 3 1 1 2 1-3 Referring to, there are shown various views of an antenna structure, in accordance with an embodiment. The antenna structurecan be used in a systemfor generating and steering an OAM beam, such as the one shown in. The antenna structureofincludes three circular radial waveguides, namely, a first radial waveguide, a second radial waveguide, and a central radial waveguide. The three radial waveguidesare concentrically stacked about a longitudinal axisof the antenna structure, in a nested arrangement with respect to one another. Specifically, the central radial waveguideis concentrically nested within the first radial waveguide, and the first radial waveguideis concentrically nested within the second radial waveguide. Each one of the radial waveguidesis configured to operate as a radial line slot array (RLSA) antenna.

108 120 120 2 2 FIGS.A-G 1-3 2 It is appreciated that while antenna structuredepicted inincludes three radial waveguides, it is contemplated that other embodiments may include fewer or more radial waveguides. For example, a first additional radial waveguide could be provided within which the second radial waveguidewould be nested, a second additional radial waveguide could be provided within which the first additional radial waveguide would be nested, and so on for any further additional radial waveguide.

108 102 108 102 102 120 1-3 In some embodiments, the antenna structuremay be configured to output the OAM beamwith a circular polarization. In other embodiments, the antenna structuremay be configured to output the OAM beamwith a linear polarization. The polarization of the OAM beammay be determined by the slot arrangement of the radial waveguides.

120 128 130 128 130 132 128 130 132 128 130 132 118 1 1 1 1 1 1 1 1 1 1 1 1 The first radial waveguideincludes a first base plateand a first slot plate. The base plateand the slot plateare spaced apart from each other and define a first waveguide cavitytherebetween. In some embodiments, the spacing between the base plateand the slot plate, which defines the height of the first waveguide cavitymay be of the order of about 0.1 mm to about 300 mm. The base plateand the slot platemay each be made of metal (e.g., aluminum) or another suitable electrically conductive material. The first waveguide cavitymay be filled with air or any other dielectric material within which the beamsteering signalscan propagate with suitably low losses.

120 134 128 134 120 134 134 120 134 126 134 134 134 134 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 FIGS.A-G The slot platehas a plurality of first radiating slotsformed therethrough. The base platebehaves as a ground plane and is devoid of slots formed therein. The number of radiating slotsin the slot platemay range from about 10 to about 1000. The size of the radiating slotsmay be of the order of about a quarter wavelength to about one wavelength. The radiating slotsmay define a plurality of slot pairs. Each slot pair may constitute an elementary radiating element of the first radial waveguide. In the embodiment of, the plurality of radiating slotsare distributed in a spiral arrangement about the antenna axis. In other embodiments, the plurality of radiating slotsmay be distributed in a concentric ring arrangement or any other suitable slot arrangement. The radiating slotsmay or may not all be identically sized and shaped, as desired or required. The number of slotsas well as the size, shape, orientation, and spatial arrangement of the slots, are all parameters that can be varied depending on the application.

120 136 138 136 136 136 120 138 132 136 120 138 132 138 132 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The first radial waveguideis partitioned into a plurality of first waveguide sectorsby a plurality of azimuthally spaced, radially extending first partition walls. In the illustrated embodiment, the number of first waveguide sectorsis 16. The number of first waveguide sectorsmay be different in other embodiments, as noted above. In the illustrated embodiment, the first waveguide sectorsall have the same azimuthal extent, but this is not a requirement. The first radial waveguideis referred to herein as being “partially sectorized”, as opposed to “fully sectorized”. This is because the radial extent of each one of the first partition wallsis less than the total radial extent of the first waveguide cavity, which results in partial isolation between the plurality of first waveguide sectors. In contrast, if the first radial waveguidewere fully sectorized, the radial extent of each first partition wallwould be equal to the total radial extent of the first waveguide cavity. It is noted that the height of the first partition wallsmay be equal to the height of the first waveguide cavityunder both partial and full sectorization conditions.

132 140 142 120 138 142 140 138 140 142 1 1 1 1 1 1 1 1 1 1 In the illustrated embodiment, the first waveguide cavityextends radially between an inner edgeand an outer edgeof the first radial waveguide, while each first partition wallextends radially from the outer edgebut terminates at a distance from the inner edge. However, in other embodiments, each first partition wallmay instead extend radially from the inner edgebut terminates at a distance from the outer edge. In yet other embodiments, other partition wall configurations can be implemented to achieve partial sectorization, for example, partition walls offset from both cavity edges, and multi-segment partition walls.

2 2 FIGS.A-G 136 144 144 144 136 128 126 140 142 144 120 144 106 118 144 118 136 144 118 118 136 144 142 132 134 136 136 102 118 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Referring still to, each first waveguide sectorincludes a respective first feed probe. The feed probemay be a coaxial probe, for example, an SMA coaxial feed probe. Each feed probeextends inside its corresponding waveguide sectorvia a respective opening formed through the base plate, in radial proximity to the antenna axis(or at least closer to the inner edgethan to the outer edge). The feed probesof the first radial waveguidemay be located at a plurality of evenly spaced first azimuthal positions along a first circular array. Each feed probeis connected to a corresponding output port of the beamsteering deviceto receive therefrom a corresponding one of a first subset of the beamsteering signals. Each feed probeis configured to introduce its corresponding beamsteering signalinto its corresponding waveguide sector. The feed probemay be configured to convert the electromagnetic power of the beamsteering signalfrom a TEM coaxial mode to a TEM cavity mode. This causes the beamsteering signalfed into each first waveguide sectorto propagate in the radial direction as an outward-directed electromagnetic wave. As the wave propagates from the feed probetoward the outer edgeof the first waveguide cavity, its power gradually radiates through the radiating slotsassociated with the first waveguide sector. It follows that the total power radiated from all the first waveguide sectorscombine to form a first beam component of the OAM beam. The OAM mode content and the steering direction of the first beam component are determined by the OAM phase shifts and the beamsteering phase shifts imparted to the first subset of beamsteering signals, respectively.

120 120 120 128 130 132 130 120 128 120 130 134 128 130 134 130 134 126 2 1 2 2 2 2 2 1 1 1 2 2 2 2 2 1 2 The second radial waveguideshares several features with the first radial waveguide. The second radial waveguideincludes a second base plateand a second slot platethat are spaced apart from each other and define a second waveguide cavitytherebetween. The slot platehas a cylindrical recess formed therein, within which the first radial waveguidemay be snuggly inserted. In the illustrated embodiment, the bottom surface of the cylindrical recess provides the top surface of the base plateof the first radial waveguide. The second slot platehas a plurality of second radiating slotsformed therethrough. The base platehas no slots formed therein and acts as a ground plane. Due to its larger surface area, the second slot platemay include a greater number of radiating slotsthan the first slot plate, but this is not requirement. The plurality of second radiating slotsmay be distributed in a spiral arrangement about the antenna axisbut other slot arrangements are possible, such as a concentric ring arrangement.

120 136 138 136 136 136 136 136 120 120 138 132 138 132 132 140 142 120 138 140 142 138 142 140 2 2 2 1 1 2 1 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 The second radial waveguideis partitioned into a plurality of second waveguide sectorsby a plurality of azimuthally spaced, radially extending second partition walls. In the illustrated embodiment, the number of second waveguide sectorsis 32. The number of second waveguide sectorsmay be different in other embodiments, as noted above. The number of second waveguide sectorsmay be greater than the number of first waveguide sectors, but this is not a requirement. In the illustrated embodiment, the second waveguide sectorsall have the same azimuthal extent, but this is not a requirement. Like the first radial waveguide, the second radial waveguideis partially sectorized. This is because the radial extent of each second partition wallis less than the total radial extent of the second waveguide cavity. The height of the second partition wallsmay be equal to the height of the second waveguide cavityunder both partial and full sectorization conditions. In the illustrated embodiment, the second waveguide cavityextends radially between an inner edgeand an outer edgeof the second radial waveguide, while each second partition wallextends radially from the inner edgebut terminates at a distance from the outer edge. However, in other embodiments, each second partition wallmay instead extend radially from the outer edgebut terminates at a distance from the inner edge. Other partition wall configurations can be used in other embodiments, as noted above.

120 108 1-2 It is noted that providing the first and second radial waveguideswith a partial sectorized configuration can improve or at least mitigate deterioration in the radiation performances of the antenna structurecompared to a full waveguide sectorization, for example, in terms of suppressing or at least reducing grating lobes and/or side lobes.

136 144 144 136 128 126 140 142 144 120 144 106 118 144 118 136 118 134 136 102 118 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Each second waveguide sectorincludes a respective second feed probe. Each feed probeextends inside its corresponding waveguide sectorvia a respective opening formed through the base plate, in radial proximity to the antenna axis(or at least closer to the inner edgethan to the outer edge). The feed probesof the second radial waveguidemay be located at a plurality of evenly spaced second azimuthal positions along a second circular array. Each feed probeis connected to a corresponding output port of the beamsteering deviceto receive therefrom a corresponding one of a second subset of the beamsteering signals. Each feed probeis configured to introduce its corresponding beamsteering signalinto its corresponding waveguide sector, where beamsteering signalis caused to propagate in the radial direction as an outward-directed electromagnetic wave and to gradually radiates its power through the corresponding radiating slots. It follows that the total power radiated from all the second waveguide sectorscombine to form a second beam component of the OAM beam. The OAM mode content and the steering direction of the second beam component are determined by the OAM phase shifts and the beamsteering phase shifts imparted to the first subset of beamsteering signals, respectively. In some embodiments, the second beam component may carry one or more second OAM modes of higher order than one or more first OAM modes carried by the first beam component.

120 120 120 128 130 132 130 120 120 128 120 130 134 128 130 134 130 134 126 3 1-2 3 3 3 3 1 1 3 3 3 2 3 3 3 3 1-2 3 The central radial waveguideis not sectorized but still shares several features with the first and second radial waveguides. The central radial waveguideincludes a central base plateand a central slot platethat are spaced apart from each other and define a central waveguide cavitytherebetween. The slot plateof the first radial waveguidehas a cylindrical recess formed therein, which the central radial waveguidemay be snuggly inserted. In the illustrated embodiment, the bottom surface of the cylindrical recess provides the top surface of the base plateof the central radial waveguide. The central slot platehas a plurality of central radiating slotsformed therethrough. The base platehas no slots formed therein and acts as a ground plane. Due to its smaller surface area, the central slot platemay include a smaller number of radiating slotsthan the first and second slot plates, but this is not requirement. The plurality of third radiating slotsmay be distributed in a spiral arrangement about the antenna axisbut other slot arrangements are possible, such as a concentric ring arrangement.

120 144 144 126 132 128 144 106 118 144 118 132 144 142 132 134 102 120 144 102 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 The central radial waveguideincludes a feed probe. The feed probeextends coaxially with the antenna axisand protrudes inside the central waveguide cavityvia a respective opening formed through the base plate. The feed probeis connected to a corresponding output port of the beamsteering deviceto receive therefrom an unsteering one of the beamsteering signals. The feed probeis configured to introduce the unsteering signalinside the central waveguide cavityfor radial propagation therein as an outward-directed electromagnetic wave. As the wave propagates from the feed probetoward the outer edgeof the central waveguide cavity, its power gradually radiates through the central radiating slotsto form a third beam component of the OAM beam. Because the central radial waveguideis not sectorized and includes a single feed probe, the third beam component may not be steered and may thus be referred to as an “unsteered” beam component of the OAM beam.

108 146 132 146 146 142 120 1-3 1-3 1-3 2 2 FIGS.A-G In some embodiments, the antenna structurecan include one or more electromagnetic-radiation absorbersdisposed at various locations within the waveguide cavities. The one or more electromagnetic-radiation absorbersare configured to absorb electromagnetic radiation incident thereon and prevent unwanted leakage of electromagnetic energy within or outside the antenna structure. In the embodiment of, electromagnetic-radiation absorbersare provided along the outer edgesof the radial waveguides, but other arrangements are contemplated in other embodiments.

2 2 FIGS.A-G 106 118 118 118 16 144 120 118 32 144 120 118 144 120 104 116 118 1162 118 1163 118 104 106 1-3 1-3 1 1 1 2 2 2 3 3 3 1 1 2 3 In the embodiment of, the beamsteering deviceis configured to output 49 beamsteering signals. The 49 beamsteering signalsinclude: (i) a first subset of 16 beamsteering signals, which are directed to thefeed probesof the first radial waveguide; (ii) a second subset of 32 beamsteering signals, which are directed to thefeed probesof the second radial waveguide; and (ii) a single unsteering signal, which is directed to the single feed probeof the central radial waveguide. In this embodiment, the beamforming devicemay be configured to generate: (i) a first subset of 16 beamforming signalsassociated with the first subset of 16 beamsteering signals(e.g., using a 16×16 Butler matrix); (ii) a second subset of 32 beamforming signalsassociated with the second subset of 32 beamsteering signals(e.g., using a 32×32 Butler matrix); and (iii) a single beamforming signalassociated with the single unsteering signal(e.g., using a single signal line passing between the two devices,).

2 2 FIGS.A-G 130 148 130 148 130 148 148 150 134 134 134 134 1 1 2 2 3 3 1-3 2 1 1 3 In the embodiment of, the top surface of the first slot platedefines a first radiating surface, the top surface of the second slot platedefines a second radiating surface, and the top surface of the central slot platedefines a central radiating surface. Furthermore, the first, second, and central radiating surfacesare substantially coplanar with one another in order to define a flat common radiating surfaceof the antenna structure. In such an arrangement, the depth of the second radiating slotsis greater than the depth of the first radiating slots, and the depth of the first radiating slotsis greater than the depth of the central radiating slots.

108 150 120 148 150 126 150 144 148 134 108 108 150 1-3 1-3 1-3 1-3 1-3 It is noted that providing the antenna structurewith a flat radiating surfaceby stacking multiple concentric radial waveguidesin a nested arrangement can achieve several advantages compared to a multilevel arrangement of the waveguide's radiating surfaces. One advantage is that a flat radiating surfacecan reduce near-field interference in proximity to the antenna axisbetween the OAM modes (particularly lower-order modes) generated by the larger radial waveguide(s) and the OAM modes generated by the smaller radial waveguide(s). If left uncontrolled, such near-field interference effects can cause unwanted reflections and other radiation performance deterioration. Another advantage of a flat radiating surfaceis that it can facilitate impedance matching of the feed probes. This is because in a single-level arrangement of the waveguide's radiating surfaces, all the radiating slotsshould be exposed to substantially identical environmental conditions. This can increase the uniformity of the load impedance (e.g., 377Ω) across the antenna structureand improve the reflection coefficient of the antenna structure. Yet another advantage of a flat radiating surfaceis that it can provide a more compact arrangement and facilitate packaging. It is noted that the disclosed techniques contemplate flat-radiating-surface antenna structures that include more than two sectorized radial waveguides stacked in a nested arrangement.

144 144 144 144 144 144 144 144 2 1 1 2 1 2 1,n 1 1 1 2,n 2 2 2 th th In some embodiments, the plurality of second feed probesmay be azimuthally offset relative to a plurality of first feed probes. In such embodiments, the plurality of first feed probesare located at a plurality of first azimuthal positions, the plurality of second feed probesare located at a plurality of second azimuthal positions, and each first azimuthal position is different from each second azimuthal position. The provision of an azimuthal offset between the arrangement of the first feed probesand the second feed probescan be advantageous in terms of improving or at least mitigating adverse effects in load termination performance. In some embodiments, the azimuthal position φof the nfirst feed probe can be given by 2π(n−1)/N, where Nis the number of first feed probes(e.g., 16 in the illustrated embodiment) in the first radial waveguide, and wherein the nsecond azimuthal position φis given by π(2n−1)/N, where Nis the number of second feed probes(e.g., 32 in the illustrated embodiment). These relationships can be generalized to the case of P>2 concentric circular arrays of feed probes as follows:

p,n p th th th where φis the azimuthal position of the nfeed probe of the pcircular array, Nis the total number of feed probes in the pcircular array, and the circular array radius increases as p increases.

3 FIG. 3 FIG. 152 154 144 154 144 154 144 144 152 1 1 1 2 2 2 3 3 3 4 Referring to, there is illustrated an exemplary of three concentric circular feed probe arrays(P=3), where the first probe array(p=1) includes four feed probes(N=4), the second probe array(p=2) includes eight feed probes(N=8), and the third probe array(p=3) includes sixteen feed probes(N=16).also includes a single feed probelocated at the center of the feed probe arrays.

108 144 120 126 134 120 126 144 120 134 136 1-2 1-2 1-2 1-2 1-2 1-2 1-2 1-2 In some embodiments, waveguide sectorization, whether partial or full, can result in less-than-optimal operation. For example, waveguide sectorization can generate unwanted grating lobes that can undesirably or adversely impact the radiation performance of the antenna structure. In some embodiments, such potential issues or limitations can be overcome or mitigated using different approaches. Non-limiting examples of such approaches may include (i) moving the feed probesof the sectorized radial waveguidesfurther from the antenna axis; (ii) moving the radiating slotsof the sectorized radial waveguidescloser to the antenna axis; (iii) increasing the number of feed probesin each sectorized radial waveguide; and (iv) increasing the number of radiating slotsin each waveguide sector.

4 4 5 6 6 7 7 8 8 FIGS.A-C,,A-C,A-C, andA-C 1 FIG. 108 100 Various other embodiments will be now described with reference to. Each of these embodiments depicts an antenna structurethat can be used in a systemfor generating and steering an OAM electromagnetic beam, such as the one shown in. Each of these embodiments shares several features with previously described embodiments but differ in certain respects. Such shared features will not be described in detail again other than to highlight their differences.

4 4 FIGS.A-C 4 4 FIGS.A-C 2 2 FIGS.A-G 108 108 108 120 1 are different views of an antenna structure, in accordance with an embodiment. The antenna structureofdiffers from the antenna structureofin that it does not include a central radial waveguide nested within the first radial waveguideand configured to generate an unsteered beam component (e.g., a zeroth-order OAM beam component).

108 150 148 120 120 120 2 2 4 4 FIGS.A-G andA-C 1-2 1-2 1 2 It is noted that the antenna structuresshown ininclude both: (i) a flat radiating surfacecombining the radiating surfacesof at least two sectorized radial waveguides; and (ii) partially sectorized radial waveguides-. However, embodiments that use either one of these two features, but not both, are contemplated by the present disclosure. Non-limiting examples of such embodiments are described below.

5 FIG. 2 2 FIGS.A-G 5 FIG. 108 108 120 120 136 138 120 136 138 138 132 138 132 1-2 1 1 1 2 2 2 1 2 2 is a partially exploded perspective view of an antenna structure, in accordance with an embodiment. In contrast to the antenna structureof, the first and second radial waveguidesof the antenna structure ofare fully, rather than partially, sectorized. Specifically, the first radial waveguideis partitioned into a plurality of first waveguide sectorsby a plurality of azimuthally spaced extending first partition walls, and the second radial waveguideis partitioned into a plurality of second waveguide sectorsby a plurality of azimuthally spaced extending second partition walls. The radial extent of each first partition wall, is equal to the total radial extent of the first waveguide cavity, and the radial extent of each second partition wallis equal to the total radial extent of the second waveguide cavity.

6 6 7 7 8 8 FIGS.A-C,A-C, andA-B 108 108 120 1 depict three other embodiments of an antenna structure. In each of these three embodiments, the antenna structureincludes a partially sectorized first radial waveguidebut does not include a flat radiating surface combining the radiating surfaces of at least two (partially or fully) sectorized radial waveguides.

6 6 FIGS.A-C 108 120 1 In, the antenna structureincludes a single radial waveguide, namely a first radial waveguidewith partial sectorization.

7 7 FIGS.A-C 108 120 120 120 148 120 148 120 1 3 1 1 1 3 3 In, the antenna structureincludes a first radial waveguidewith partial sectorization, and a central radial waveguidenested within the first radial waveguide. In this embodiment, the radiating surfaceof the first radial waveguideand the radiating surfaceof the central radial waveguideare substantially coplanar with each other.

8 8 FIGS.A-C 108 120 120 120 148 120 148 120 1 3 1 1 1 3 3 In, the antenna structureincludes a first radial waveguidewith partial sectorization, and a central radial waveguidestacked on top of the first radial waveguidein a multilevel arrangement. In this embodiment, the radiating surfaceof the first radial waveguideand the radiating surfaceof the central radial waveguideare not coplanar with each other.

9 FIG. 9 FIG. 200 200 200 Referring to, there is illustrated a flow diagram of a methodof generating and steering an OAM beam. The methodofmay be implemented in a system such as those described above, or another suitable system. It is noted that the methodmay share many features similar to those described with respect to the structure, configuration, and operation of system implementations. Such similar features need not be described again below.

200 202 202 The methodincludes a stepof generating a plurality of beamforming signals by modulating a plurality of input signals in accordance with beamforming phase shifts related to a mode content of the OAM beam. In some embodiments, the generating stepincludes an operation of adjusting the beamforming phase shifts to change the mode content of the OAM beam.

200 204 204 The methodalso includes a stepof generating a plurality of beamsteering signals by modulating the plurality of beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM beam. In some embodiments, the generating stepincludes an operation of adjusting the beamsteering phase shifts to change the steering conditions for the OAM beam. In some embodiments, the steering conditions may be set or adjusted within an azimuth angle steering range ranging from about 0° to about 360° and/or within an elevation angle steering range ranging from about 0° to about 10°.

200 206 206 The methodfurther includes a stepof emitting the OAM beam according to the steering conditions by feeding the plurality of beamsteering signals to an antenna structure. The antenna structure includes a radial waveguide defining a waveguide cavity and having a slot plate with a plurality of radiating slots formed therethrough. The radial waveguide is partitioned into a plurality of angular waveguide sectors by a plurality of partition walls. Each partition wall extends radially over less than a radial extent of the waveguide cavity, thereby providing partial waveguide sectorization. The emitting stepincludes an operation of introducing a corresponding one of the beamsteering signals into each waveguide sector to cause the corresponding beamsteering signal to radiate through a number of the radiating slots corresponding to the waveguide sector, thereby generating the OAM beam.

206 200 In some embodiments, the radial waveguide is a first radial waveguide configured to generate a first beam component of the emitted OAM beam from a first subset of the beamsteering signals, and the antenna structure further includes a second radial waveguide azimuthally enclosing the first radial waveguide. The second radial waveguide defines a waveguide cavity and has a slot plate with a plurality of radiating slots formed therethrough. The second radial waveguide is partitioned into a plurality of angular waveguide sectors by a plurality of partition walls. Each partition wall extends radially over less than a radial extent of the waveguide cavity. In such embodiments, the emitting stepmay further include an operation of introducing a corresponding one of a second subset of the beamsteering signals into each waveguide sector of the second radial waveguide to cause the corresponding beamsteering signal to radiate through a number of the radiating slots of the second radial waveguide corresponding to the waveguide sector, thereby generating a second beam component of the emitted OAM beam. In some embodiment, the slot plate of the first radial waveguide defines a first radiating surface, and the slot plate of the second radial waveguide defines a second radiating surface. In such embodiments, the methodmay further include an operation of providing the first radiating surface and the second radiating surface in a substantially coplanar arrangement.

206 In some embodiments, the radial waveguide is a first radial waveguide configured to generate a first beam component of the emitted OAM beam, and the antenna structure further includes a central radial waveguide nested within the first radial waveguide. The central radial waveguide defines a waveguide cavity and has a slot plate having a plurality of radiating slots formed therethrough. In such embodiments, the emitting stepmay further include an operation introducing a corresponding one of the beamsteering signals into the central radial waveguide to cause the corresponding beamsteering signal to radiate through the radiating slots of the central radial waveguide and generate an unsteered beam component of the emitted OAM beam. In some embodiments, the unsteered beam component of the OAM beam is a zeroth-order OAM mode.

10 FIG. 10 FIG. 300 300 300 Referring to, there is illustrated a flow diagram of another methodof generating and steering an OAM beam. The methodofmay be implemented in a system such as those described above, or another suitable system. It is noted that the methodmay share many features similar to those described with respect to the structure, configuration, and operation of system implementations. Such similar features need not be described again below.

300 302 302 The methodincludes a stepof generating a plurality of beamforming signals by modulating a plurality of input signals in accordance with beamforming phase shifts related to a mode content of the OAM beam. In some embodiments, the generating stepincludes an operation of adjusting the beamforming phase shifts to change the mode content of the OAM beam.

300 304 304 The methodalso includes a stepof generating a plurality of beamsteering signals by modulating the plurality of beamforming signals in accordance with beamsteering phase shifts related to steering conditions for the OAM beam. In some embodiments, the generating stepincludes an operation of adjusting the beamsteering phase shifts to change the steering conditions for the OAM beam. In some embodiments, the steering conditions may be set or adjusted within an azimuth angle steering range ranging from about 0° to about 360° and/or within an elevation angle steering range ranging from about 0° to about 10°.

300 306 306 The methodfurther includes a stepof emitting the OAM beam according to the steering conditions by feeding the plurality of beamsteering signals to an antenna structure such as described above. The antenna structure includes a first radial waveguide and a second radial waveguide. The second radial waveguide azimuthally encloses the first radial waveguide. The first radial waveguide includes a first base plate and a first slot plate defining a first waveguide cavity therebetween. The first slot plate has a plurality of first radiating slots formed therethrough. The first radial waveguide is partitioned into a plurality of first waveguide sectors by a plurality of azimuthally spaced, radially extending first partition walls. The second radial waveguide includes a second base plate and a second slot plate defining a second waveguide cavity therebetween. The second slot plate has a plurality of second radiating slots formed therethrough. The second radial waveguide is partitioned into a plurality of second waveguide sectors by a plurality of azimuthally spaced, radially extending second partition walls. The first slot plate defines a first radiating surface, and the second slot plate defines a second radiating surface, The first radiating surface and the second radiating surface are substantially coplanar with each other. The emitting stepincludes a first operation and a second operation. The first operation includes introducing a corresponding one of a first subset of the beamsteering signals into each first waveguide sector to cause the corresponding beamsteering signal to radiate through a number of the first radiating slots corresponding to the first waveguide sector. The first operations generate a first beam component of the OAM beam. The second operation includes introducing a corresponding one of a second subset of the beamsteering signals into each second waveguide sector to cause the corresponding beamsteering signal to radiate through a number of the second radiating slots corresponding to the second waveguide sector. The second operation generates a second beam component of the OAM beam.

300 In some embodiments, the methodincludes an operation of setting or adjusting the mode content of the OAM beam to provide that the second beam component carries one or more second OAM modes of higher order than one or more first OAM modes carried by the first beam component.

In some embodiments, each first partition wall extends radially over less than a radial extent of the first waveguide cavity to provide partial isolation between the plurality of first waveguide sectors, and/or each second partition wall extends radially over less than a radial extent of the second waveguide cavity to provide partial isolation between the plurality of second waveguide sectors.

306 In some embodiments, the antenna structure further includes a central radial waveguide nested within the first radial waveguide. The central radial waveguide defines a central waveguide cavity therebetween and includes a central slot plate having a plurality of central radiating slots formed therethrough. The central slot plate defines a central radiating surface that is substantially coplanar with the first radiating surface and the second radiating surface. In such embodiments, the emitting stepmay further include an operation of introducing a corresponding one of the beamsteering signals into the central radial waveguide to cause the corresponding beamsteering signal to radiate through the central radiating slots and generate an unsteered beam component of the emitted OAM beam. In some embodiments, the unsteered component may be a zeroth-order OAM mode.

The following description reports computations and numerical simulations conducted to study and investigate certain aspects of the disclosed embodiments. It is appreciated that the systems and methods disclosed herein may have a number of features, variations, and applications. As such, the following description is provided to further illustrate some aspects and capabilities of the techniques disclosed, but should not be construed as in any way limiting their scope.

11 FIG. 2 2 FIGS.A-G 11 FIG. shows simulated radiation patterns for several OAM modes (k=±1, ±2, ±3) obtained using a beam generation and system in accordance with an embodiment. The system has an antenna structure similar to the one depicted inthat includes a first partially sectorized radial waveguide, a second partially sectorized radial waveguide, and a central radial waveguide concentrically stacked in a nested arrangement. The OAM modes shown inare generated by the first radial waveguide, which is azimuthally partitioned into 16 waveguide sectors.

12 FIG. 2 2 FIGS.A-G 12 FIG. shows simulated radiation patterns for several OAM modes (k=±4, ±6, ±8) obtained using a beam generation and system in accordance with an embodiment. The system has an antenna structure similar to the one depicted inthat includes a first partially sectorized radial waveguide, a second partially sectorized radial waveguide, and a central radial waveguide concentrically stacked in a nested arrangement. The OAM modes shown inare generated by the second radial waveguide, which is azimuthally partitioned into 32 waveguide sectors.

13 13 FIGS.A-E 2 2 FIGS.A-G 13 13 FIGS.A-E show simulated far-field radiation patterns for five different OAM modes (k=+2, +4, +6, +8, +10) using a beam generation and steering system in accordance with an embodiment. The system has an antenna structure similar to the one depicted inthat includes a first partially sectorized radial waveguide, a second partially sectorized radial waveguide, and a central radial waveguide concentrically stacked in a nested arrangement. The OAM modes shown inare generated by the second radial waveguide, which is azimuthally partitioned into 32 waveguide sectors. For each OAM mode, the simulated radiation patterns have been steered to four different azimuthal angles (φ=0°, 90°, 180°, 360°) without varying the elevation angle θ.

14 14 FIGS.A-B 2 2 FIGS.A-G 14 14 FIGS.A-B show simulated far-field radiation patterns for two different OAM modes (k=±2) using a beam generation and steering system in accordance with an embodiment. The system has an antenna structure similar to the one depicted inthat includes a first partially sectorized radial waveguide, a second partially sectorized radial waveguide, and a central radial waveguide concentrically stacked in a nested arrangement. The OAM modes shown inare generated by the second radial waveguide, which is azimuthally partitioned into 32 waveguide sectors. For each OAM mode, the simulated radiation patterns have been steered to four different elevation angles (θ=0°, 3°, 6°, 10°) without varying the elevation angle θ.

The term “processor” as used herein is intended to refer broadly to any electronic device, circuitry, or component capable of processing, receiving, or transmitting data or instructions, such as computer programs, commands, functions, processes, software codes, executables, applications, and the like. The term “processor” is meant to include a single processor or a single processing unit, multiple processors or multiple processing units, or other suitably configured processing element or elements. Where a processor includes a plurality of processing elements, the processing elements may all be located at one site, or they may be distributed across multiple sites and interconnected by a communication network. Examples communication networks include a local area network (LAN) and a wide area network (WAN), such as, the Internet. Non-limiting examples of a processor include a general-purpose single- or multi-core processor; a central processing unit (CPU); a microprocessor; a controller; a microcontroller; a digital signal processor (DSP); a programmable logic device; a field-programmable gate array (FPGA); an application-specific integrated circuit (ASIC); a digital processor or circuit; an analog processor or circuit; state machine; and/or any other device capable of processing information.

The term “memory” as used herein is intended to refer broadly to any electronic device, circuitry, or component capable of storing electronic data or information. In some instances, the term “memory” may be used interchangeably with the term “computer readable storage medium”. The term “memory” is meant to include a single memory or a single memory unit, multiple memories or multiple memory units, or other suitably configured memory element or elements. Where a memory includes a plurality of memory elements, the memory elements may all be located at one site, or they may be distributed across multiple sites and interconnected by a communication network. Non-limiting examples of a memory include a random-access memory (RAM) of any type; a read-only memory (ROM) of any type; a magnetic storage device; an optical storage device; a solid-state drive (SSD) device, such as a flash drive memory; or any other tangible and/or non-transitory computer readable medium which can be used to store electronic data or information.

In the present disclosure, similar elements in the drawings have been given similar reference numerals. For clarity and ease of illustration, some elements may not be identified in a certain figure if they are already identified in another figure. The elements of the drawings are not necessarily depicted to scale. Positional descriptors indicating the arrangement of one element should be taken in the context of the figures and should not be considered limiting.

The terms “a”, “an”, and “one” are defined herein to mean “one or more”, that is, these terms do not exclude a plural number of elements, unless explicitly stated otherwise herein. The term “or” is defined herein to mean “and/or”, unless explicitly stated otherwise herein.

The expressions “at least one of A, B, and C”, “one or more of A, B, and C”, or any other variant thereof, are understood to include A alone, B alone, and C alone, a combination of A and B, a combination of A and C, a combination of B and C, or a combination of A, B, and C.

Terms such as “substantially”, “generally”, “approximately”, “about”, or any other variant thereof, which modify a value, condition, or characteristic of a feature of an aspect or embodiment disclosed herein, should be understood to mean that the value, condition, or characteristic is defined within tolerances that are acceptable for the proper operation of this aspect or embodiment and/or that fall within an acceptable range of experimental error. In particular, the term “about” generally refers to a range of numbers that one skilled in the art would consider equivalent to the stated value (e.g., having the same or an equivalent function or result). In some cases, the term “about” means a variation within ±10% of the stated value. It is noted that all numeric values used herein are assumed to be modified by the term “about”, unless otherwise stated or dictated by context.

The terms “connected” and “coupled”, and derivatives and variants thereof, refer herein to any connection or coupling, either direct or indirect, between two or more elements, unless otherwise stated or dictated by context. For example, the connection or coupling between the elements may be mechanical, optical, electrical, magnetic, thermal, chemical, logical, fluidic, operational, or any combination thereof.

Numerous modifications could be made to the features of any embodiments described herein without departing from the scope of the appended claims. Furthermore, any feature of any embodiment disclosed herein can be combined or used with any feature of any other embodiment disclosed herein, unless otherwise stated or dictated by context.